JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int_{-1}^1 \frac{(1+\sqrt{|x|-x}) e^x+(\sqrt{|x|-x}) e^{-x}}{e^x+e^{-x}} d x\) is equal to
- A \(3-\frac{2 \sqrt{2}}{3}\)
- B \(2+\frac{2 \sqrt{2}}{3}\)
- C \(1-\frac{2 \sqrt{2}}{3}\)
- D \(1+\frac{2 \sqrt{2}}{3}\)
Answer & Solution
Correct Answer
(D) \(1+\frac{2 \sqrt{2}}{3}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int_{-1}^1 \frac{(1+\sqrt{|-\mathrm{x}|-(-\mathrm{x})}) \mathrm{e}^{-\mathrm{x}}+(\sqrt{|-\mathrm{x}|-(-\mathrm{x})}) \mathrm{e}^{-(-\mathrm{x})}}{\mathrm{e}^{-\mathrm{x}}+\mathrm{e}^{-(-\mathrm{x})}} \mathrm{dx} \)…
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